Bran's ability to see different moments in time has led to speculations about his power to change the timeline of events. In the storyline of Hodor, for example, it gets clear that Bran's actions during the visions can carry a real impact into the future lives of those he interacts with.
One of the theories about the final season of Game of Thrones states that Bran might have stayed for too long inside the visions from the birth of the Night King, while attempting to find a way to defeat him. So long that he "drawned", meaning he would no be longer capable of dissociating himself from the Night King, stablishing a warg-like relationship he is unable to break and which keeps both connected for thousands of years, until the current days.
If such connection between Bran and the Night King proves to be right, or if it is shown that one cannot die without the other dying as well, this question will be resolved as "Yes".